Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions.
type: Item
instance of: scholarly article
title: Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions.
zbMATH Open document ID: 1347.20054
DOI: 10.4171/JEMS/471
author: Elena Fuchs
author: Chen Meiri
author: Peter Sarnak
published in: Journal of the European Mathematical Society (JEMS)
publication date: 2014-10-31T00:00:00Z
full work available at URL: https://arxiv.org/abs/1305.0729
review text: Summary: We give a criterion which ensures that a group generated by Cartan involutions in the automorph group of a rational quadratic form of signature \((n-1,1)\) is ``thin'', namely it is of infinite index in the latter. It is based on a graph defined on the integral Cartan root vectors, as well as Vinberg's theory of hyperbolic reflection groups. The criterion is shown to be robust for showing that many hyperbolic hypergeometric groups for \(_nF_{n-1}\) are thin.
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 20F67
Mathematics Subject Classification ID: 14D05
Mathematics Subject Classification ID: 33C20
zbMATH DE Number: 6363149
zbMATH Keywords: hypergeometric monodromy
zbMATH Keywords: hyperbolic groups
zbMATH Keywords: Cartan involutions
zbMATH Keywords: hypergeometric functions
MaRDI profile type: Publication
arXiv ID: 1305.0729
cites work: Monodromy for the hypergeometric function \(_ nF_{n-1}\)
cites work: Q4177654
cites work: A note on optimal unimodular lattices
cites work: \(p\)-adic cycles
cites work: Q4368847
cites work: The ubiquity of thin groups
cites work: The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces
cites work: Q3287385
cites work: Q3997989
cites work: Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros
cites work: Q3889139
cites work: Self-correspondences of \(K3\) surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups
cites work: Q4462785
cites work: Q3409184
cites work: Q5439504
cites work: Arithmeticity of certain symplectic hypergeometric groups
cites work: ON GROUPS OF UNIT ELEMENTS OF CERTAIN QUADRATIC FORMS
cites work: Q3722747
description: scientific article; zbMATH DE number 6363149